Sounds to me like your instrument should be treated to a good set-up, meaning the string height set, nut slots optimised, saddle positions corrected for intonation, neck relief set (with trussrod), frets crowned and polished properly, and whatever else a decent tech will do. These things aren't necessarily completed at the factory, and need to be revisited periodically over time. Your instrument CAN be set-up right and you'll appreciate it even more.
Most any electronic tuner will do the job you require of it, ie tune open strings, but check octaves and some fretted pitches to be sure.